# Formulas and Shortcuts for Time, Speed and Distance

Problems on** ‘Time, Speed and Distance’ **are very common in competitive exams like **Banking, SSC, CSAT, etc. **Knowing the shortcut methods for solving such **Quantitative Aptitude** problems will give you an edge as most competitive exams also test your time management skills. The basic concepts of ‘Time, Speed and Distance’ revolve around its formula;

For example, if you know the speed of any vehicle and the distance covered by that vehicle, then you can easily calculate the time taken for the entire journey by using the above formula.

Let's have a look at some basic formulas and shortcut methods for problems related to Time, Speed and Distance:

**Learn shortcuts to solve Problems on Trains**

**Basic Conversions**

**Example**: A train travelling at the rate of 72 km/hr crosses a pole in 8 seconds. What is its length?

**Solution: **

**Average Speed**

The basic formula for average speed is:

That is,

**• When distance is constant: **

**• When distance is constant:**

The average speed is given by the formula,

where S_{1}, S_{2},… S_{n} are the different speeds.

**For two speeds,**

where S_{1} and S_{2} are the two different speeds.

For example, if a car travels distance (d) at a speed of x km/hr and returns at y km/hr, then the above formula can be used to calculate the average speed.

**• When time is constant:**

**• When time is constant:**

The average speed is given by the formula,

**For two speeds,**

**Relative speed:**

The relative speed of two bodies travelling at speeds of x km/hr and y km/hr:

**• in the same direction is given by (x - y)km/hr**

**• in the opposite direction is given by (x + y)km/hr**

**Example:** A man rides a motor cycle for 11 km at 20 km/hr and for 20 km at 11 km/hr. What is the average speed of both his trips?

**Solution: **

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